In this paper, we study flowshop scheduling problems with availability constraints. In such problems, n jobs have to be scheduled on m machines sequentially under assumption that the machines are unavailable during some periods of planning horizon. The objective of the problem is to find a non-permutation schedule which minimizes the makespan. As a solution procedure, we propose an improved genetic algorithm which utilizes a look-ahead schedule generator to find good solutions in a reasonable time Computational experiments show that the proposed genetic algorithm outperforms the existing genetic algorithm.